Doubt in breakpoint construction

Question

This question is from September 09, 2022 paper.

In 6)b) breakpoint construction, why is there an outgoing transition with input b from q2 to q3 and why is the q set of q3 empty - it is because there is no immediate successor for the accepting state s3 with input b and only state s2 has a successor with input b? What logic I am missing here? 

Answer 1

The successor state of a state (Q,Qf) with input σ is defined as (sucσ∃(Q),sucσ∃(Q)∩F) if Qf={}, and as (sucσ∃(Q),sucσ∃(Qf)∩F) otherwise.

In case of state q2=({s2,s3},{s3}) and input b, we therefore get 

q3 := (sucσ∃(Q),sucσ∃(Qf)∩F) 
    = (sucσ∃({s2,s3}),sucσ∃({s3})∩{s3}) 
    = ({s2,s3},{}∩{s3})
    = ({s2,s3},{})

Comments

Thank you very much for clarifying!:)